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Implicit WENO shock capturing scheme for unsteady flows. Application to one‐dimensional Euler equations
Author(s) -
Cadiou A.,
Tenaud C.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.685
Subject(s) - total variation diminishing , shock tube , discretization , euler equations , shock wave , euler's formula , shock (circulatory) , mathematics , solver , computational fluid dynamics , computer science , mathematical analysis , mechanics , physics , mathematical optimization , medicine
The unsteady numerical simulation of one‐dimensional shock waves is investigated using high‐order convective TVD and WENO schemes. Emphasis is put on the capability of existing explicit and implicit time discretization to capture the correct shock velocity. A new implicit solver is then proposed based on the WENO approach. This scheme is presented for one‐dimensional problems, but is easily extended to multi‐dimensional cases. The implicit WENO scheme is tested against the classical TVD schemes for the case of the shock tube and shock‐entropy wave interaction. Copyright © 2004 John Wiley & Sons, Ltd.